I didn't spot what Menzies were going to charge you from Corozal to Placencia. How will you get from CUN to Corozal? Have you asked Menzies for a quote for the entire journey? Especially if you tell them beforehand that you want to explore along the way, they will make all sorts of detours for you for not a lot of extra money. You will have to make the first leg, from CUN to Corozal, by road as there's no plane (unless things have changed very recently).
An alternative is the flight, which of course will be much quicker, though with two stopovers where you'll have to wait for planes. If you do end up flying via San Pedro, try to have at least three hours there to look around. You won't want to hang around either the Municipal or International airports in Belize City longer than the plane scheduling forces you to, but if you do have to hang around at the Municipal you'll find the Maya building much more comfortable than Tropic's.
The road from Belize City to Placencia, especially the part after Belmopan, is very pretty and it will be a shame to miss it. The road from Corozal to Belize City is best got over as quickly as possible.
Overall I'd say it's no contest. Use Menzies for the entire journey, even if the cost goes up quite a lot to pay for the detours. Only one thing - it's a long journey from CUN to Placencia and I don't see it being done in one day. Even flying the three legs from Corozal the rest of the way on top of a 5 hour road journey to get there from CUN will make for a long day. Do you know when you'll be able to depart CUN?
It may seem an outlandish suggestion, but with four of you have you investigated the cost of a private plane charter from CUN all the way to Placencia? It won't be a cheap option, but bearing in mind the costs you're going to incur for an overnight stay if you go surface, and of course the time it'll take, you may find the sums work out better than you think.
You can fly from CUN direct to Flores in Guatemala, which will leave you a road journey up to the Belize border (maybe 2 1/2 hours), then via Belmopan to Placencia (maybe 5 hours). Or it may be that the Tropic and Maya flights to Flores have recommenced by then, in which case you could make the entire journey by air (with changes in Flores and Belize City). I don't know whet the cost would be, but you can probably work it out from their websites. Tropic and Maya charge the same fares but do operate different schedules, so choose based on convenience of timings.